Topology and geometry of unorganized point clouds

We present a new method for defining neighborhoods, and assigning principal curvature frames, and mean and Gauss curvatures to the points of an unorganized oriented point-cloud. The neighborhoods are estimated by measuring implicitly the surface distance between points. The 3D shape recovery is based on conformal geometry, works directly on the cloud, does not rely on the generation of polygonal, or smooth models. Test results on publicly available synthetic data, as ground truth, demonstrate that the method compares favorably to the established approaches for quantitative 3D shape recovery. The proposed method is developed to serve applications involving point based rendering and reliable extraction of differential properties from noisy unorganized point-clouds.